There are mixed seeds, you can get most of the seeds that way and the rest is dropped in skull cavern. The only ones unobtainable without buying seeds are hops, the flowers and amaranth. So it is possible to finish the community center without buying seeds with remixed bundles...
Melon and pumpkin are rewards from the museum (starfruit too), blueberry, green bean and tomato (and other seeds, fruit trees) can be dropped in treasure rooms in skull cavern.
The rare crops bundle can be completed with ancient fruit, and that is a drop in the mines. No need for sweet gem berry there.
Hops isn't a problem, as far as I can see, it is only needed for the brewers bundle or wild medicine and both can be completed, because there is one option you don't need to fulfill.
The dye bundle, chef bundle and the garden bundle ask for amaranth and flowers, so I would need a seed without those or just in specific combinations.